Yes the CAA do look
When I was going for the CPL myself and a mate put the log books into the CAA at the same time , I was instructing at the time and he had perchased an aircraft to get his hours.
My log book came back quite quickly (for the CAA ) his took some time and it became clear that the CAA had checked the movment logs at a number of airfields to see if his log book entrys were genuine.